Related papers: Remarks on q-Virasoro and qKdV
This paper presents two new Weierstrass elliptic function solutions of the projective Riccati equations and four conversion formulas for converting the Weierstrass elliptic functions to the hyperbolic and trigonometric functions. The…
The quantum super-algebra structure on the deformed super Virasoro algebra is investigated. More specifically we established the possibility of defining a non trivial Hopf super-algebra on both one and two-parameters deformed super Virasoro…
A novel geometric interpretation of the solutions of the WDVV equations formerly found by A.P. Veselov is suggested.
In this note, we describe a method to construct the Picard-Vessiot ring of a given linear differential equation.
A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.
We summarize results concerning the Bernstein property of differential equations.
We systematically study Darboux-type transformations for the KdV and AKNS hierarchies and provide a complete account of their effects on hyperelliptic curves associated with algebro-geometric solutions of these hierarchies.
We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also…
In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.
For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wolff potentials.
We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
An exact formula for the solutions to the WDVV equation in terms of horizontal sections of the corresponding flat connection is found.
In this paper, we proved a special case of the DDVV Conjecture.
We discuss the question whether solutions of the initial value problem for the generalized KdV equation can have compact support at two different times.
We summarize the recent developments on the extraction of the dynamical properties of the heavy quarks from QCD spectral sum rules.
These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.
Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
It is shown that equations of the Korteweg-de Vries hierarchy and their conservation laws can be expressed via the whole powers of an integro-differential operator and functions provided by them.